1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kryger [21]
3 years ago
7

Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Mathematics
1 answer:
Anit [1.1K]3 years ago
4 0

Answer:

The answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

Step-by-step explanation:

\bold{\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]}

Solve the L.H.S part:

\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\\\\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]

After calculating the L.H.S part compare the value with R.H.S:

\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]} \\\\

\to a+2c =6....(i)\\\\\to b+2d =5....(ii)\\\\\to 3a+4c =19....(iii)\\\\\to 3b+4d = 8 ....(iv)\\\\

In equation (i) multiply by 3 and subtract by equation (iii):

\to 3a+6c=18\\\to 3a+4c=19\\\\\text{subtract}... \\\\\to 2c = -1\\\\\to  c= - \frac{1}{2}

put the value of c in equation (i):

\to a+ 2 (- \frac{1}{2})=6\\\\\to a- 2 \times \frac{1}{2}=6\\\\\to a- 1=6\\\\\to a =6 +1\\\\\to a = 7\\

In equation (ii) multiply by 3 then subtract by equation (iv):

\to 3b+6d=15\\\to 3b+4d=8\\\\\text{subtract...}\\\\\to 2d = 7\\\\\to d= \frac{7}{2}\\

put the value of d in equation (iv):

\to 3b+4 (\frac{7}{2})=8\\\\\to 3b+4 \times \frac{7}{2}=8\\\\\to 3b+14=8\\\\\to 3b =8-14\\\\\to 3b = -6\\\\\to b= \frac{-6}{3}\\\\\to b= -2

The final answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

You might be interested in
2r(2.59 + 10) - 3(r + 4) + s(r - 1)?<br> equivalent?
Bumek [7]

Answer:

2.30 is going to be your anwer

Step-by-step explanation:

7 0
3 years ago
circle 0 shown below has a radius of 27 inches.find to the nearest tenth of a degree the measure of the angle ,x, that forms are
Irina18 [472]

Answer: 29.7 degrees

Step-by-step explanation:

Good, I can see the diagram now!

First calculate circumference of the circle.

C=2πr

C=2π(27)

C=54π in ==> 360 degrees

54π/14=12.11757

360/12.11757=

29.709=29.7 degrees

8 0
2 years ago
Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student
AysviL [449]

Answer:

The mean calculated for this case is \bar X=584

And the 95% confidence interval is given by:

584-2.776\frac{86.776}{\sqrt{5}}=476.271    

584+2.776\frac{86.776}{\sqrt{5}}=691.729    

So on this case the 95% confidence interval would be given by (476.271;691.729)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=584

The sample deviation calculated s=86.776

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=5-1=4

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that t_{\alpha/2}=2.776

Now we have everything in order to replace into formula (1):

584-2.776\frac{86.776}{\sqrt{5}}=476.271    

584+2.776\frac{86.776}{\sqrt{5}}=691.729    

So on this case the 95% confidence interval would be given by (476.271;691.729)    

3 0
3 years ago
Y=-3(x+4)² + 1<br> Vertex to standard
Bess [88]

Answer:

Correct

Step-by-step explanation:

7 0
3 years ago
Approximate the real zeros of x^4-5x^3+6x^2-x-2 to the nearest tenth. a. 0.4, c. 4, 3.4 b. , 3.4 d. -4, 3.4
levacccp [35]

Answer:

x=−0.433107,3.352224

Rounding up should be -0.4 and 3.4

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in th
    14·1 answer
  • Pls help being timed
    11·2 answers
  • 25386 to the nearest 1000
    6·2 answers
  • 10. I am a number between 7 000 000 and 8 000 000.
    13·1 answer
  • Which is the LCM of (x + y) and (x + y)2.​
    5·1 answer
  • Write two numbers that multiply to the value on top and add to the value on bottom.​
    9·1 answer
  • The Great Pyramid of Giza has an approximate height of 252 yards, and the square base has side lengths of approximately 152 yard
    8·1 answer
  • HELPPP 20 PNTS
    10·1 answer
  • What is the value of b ?
    14·1 answer
  • 12 divided by 2 x the absolute value of 1.3 minus 2.16
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!